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In numerical computations, precision of floating-point computations is a keyfactor to determine the performance (speed and energy-efficiency) as well asthe reliability (accuracy and reproducibility). However, precision generallyplays a contrary role for both. Therefore, the ultimate concept for maximizingboth at the same time is the minimal-precision computing throughprecision-tuning, which adjusts the optimal precision for each operation anddata. Several studies have been already conducted for it so far (e.g.Precimoniuos and Verrou), but the scope of those studies is limited to theprecision-tuning alone. Hence, we aim to propose a broader concept of theminimal-precision computing system with precision-tuning, involving bothhardware and software stack.  In 2019, we have started the Minimal-Precision Computing project to propose amore broad concept of the minimal-precision computing system withprecision-tuning, involving both hardware and software stack. Specifically, oursystem combines (1) a precision-tuning method based on Discrete StochasticArithmetic (DSA), (2) arbitrary-precision arithmetic libraries, (3) fast andaccurate numerical libraries, and (4) Field-Programmable Gate Array (FPGA) withHigh-Level Synthesis (HLS).  In this white paper, we aim to provide an overview of various technologiesrelated to minimal- and mixed-precision, to outline the future direction of theproject, as well as to discuss current challenges together with our projectmembers and guest speakers at the LSPANC 2020 workshop;https://www.r-ccs.riken.jp/labs/lpnctrt/lspanc2020jan/.

White Paper from Workshop on Large-scale Parallel Numerical Computing  Technology (LSPANC 2020): HPC and Computer Arithmetic toward  Minimal-Precision Computing